Answer:
[tex]3^{n}+3^{n-1}[/tex]
Step-by-step explanation:
Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be [tex]x^n + yn[/tex]
Because the sequence multiplies by 3 each time, The base number in that equation would be [tex]3^n +yn[/tex].
So [tex]3^n[/tex] of the equation would be:
[tex]3, 9, 27[/tex].
Compare the 2 equations:
4, 12, 36
3, 9 ,27
The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: [tex]3^{n-1}[/tex].
Combine these 2 equations together and you get:
[tex]3^{n}+3^{n-1}[/tex].
